Numerical solutions of elliptic inverse problems via the equation error method

To estimate a parameter in an elliptic boundary value problem, the method of equation error chooses the value that minimizes the error in the PDE and boundary condition (the solution of the BVP having been replaced by a measurement). The estimated parameter converges to the exact value as the measured data converge to the exact value, provided Tikhonov regularization is used to control the instability inherent in the problem. The error in the estimated solution can be bounded in an appropriate quotient norm; estimates can be derived for both the underlying (infinite-dimensional) problem and a finite-element discretization that can be implemented in a practical algorithm. Numerical experiments demonstrate the efficacy and limitations of the method.

MULTIDIMENSIONAL OPTIMAL DROOP CONTROL FOR WIND RESOURCES IN DC MICROGRIDS

Two important and upcoming technologies, microgrids and electricity generation from wind resources, are increasingly being combined. Various control strategies can be implemented, and droop control provides a simple option without requiring communication between microgrid components. Eliminating the single source of potential failure around the communication system is especially important in remote, islanded microgrids, which are considered in this work. However, traditional droop control does not allow the microgrid to utilize much of the power available from the wind. This dissertation presents a novel droop control strategy, which implements a droop surface in higher dimension than the traditional strategy. The droop control relationship then depends on two variables: the dc microgrid bus voltage, and the wind speed at the current time. An approach for optimizing this droop control surface in order to meet a given objective, for example utilizing all of the power available from a wind resource, is proposed and demonstrated. Various cases are used to test the proposed optimal high dimension droop control method, and demonstrate its function. First, the use of linear multidimensional droop control without optimization is demonstrated through simulation. Next, an optimal high dimension droop control surface is implemented with a simple dc microgrid containing two sources and one load. Various cases for changing load and wind speed are investigated using simulation and hardware-in-the-loop techniques. Optimal multidimensional droop control is demonstrated with a wind resource in a full dc microgrid example, containing an energy storage device as well as multiple sources and loads. Finally, the optimal high dimension droop control method is applied with a solar resource, and using a load model developed for a military patrol base application. The operation of the proposed control is again investigated using simulation and hardware-in-the-loop techniques.

Evaluating the relationship between moisture induced expansion and horizontal stress orientation in samples from the nonesuch formation

High horizontal stresses can cause numerous ground control problems in mines and other underground structures ultimately impacting worker safety, productivity and the economics of an underground operation. Mine layout and design can be optimized when the presence and orientation of these stresses are recognized and their impact minimized. A simple technique for correlating the principal horizontal stress direction in a sedimentary rock mass with the preferential orientation of moisture induced expansion in a sample of the same rock was introduced in the 1970s and has since gone un-reported and unused. This procedure was reexamined at a locality near the original test site at White Pine, Michigan in order to validate the original research and to consider its usefulness in mining and civil engineering applications in high horizontal stress conditions. This procedure may also be useful as an economical means for characterizing regional stress fields.